Yes, gnocchi store well in the fridge for a day or so, or in the freezer for longer term storage. It's best to try and keep the gnocchi separate (placing on a baking sheet or tray is best) so they don't stick together, and very well covered so that they don't absorb any odours in your fridge.

If freezing, freeze on the tray until reasonably hard, and you can then transfer them to a tub or bag.

Just to expand: if you freeze them, freeze the already formed gnocchi. Do not freeze the dough ball, in my experience it was disastrous to try and make gnocchi out of it (still tasted ok, but the handling was very messy).
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nicoDec 10 '11 at 8:20